Random Variables and its Probability Distributions

A pair of dice thrown $4$ times. If getting a doublet is considered a success, find the value of $k$, if the probability of two success is $\frac{25}{k}$.

The probability that a student is not swimming is $\frac{1}{5}$. The probability that out of five students, four are swimmers is

In a box containing $100$ bulbs, $10$ are defective. The probability that out of a sample of $5$ bulbs, none is defective is

It is known that $10\%$ of certain articles manufactured are defective. What is the probability that in a random sample of $12$ such articles, $9$ are defective?

Find the probability of throwing at most $2$ sixes in $6$ throws of a single die.

Find the probability of getting $5$ exactly twice in $7$ throws of a die.

A person buys a lottery ticket in $50$ lotteries, in each of which his chance of winning a prize is $\frac{1}{100}$. If the probability that he will win a prize at least twice is $1-\left(\frac{k}{100}\right){\left(\frac{m}{100}\right)}^{49}$. Then, find the value of $\left(k+m\right)$.

A person buys a lottery ticket in $50$ lotteries, in each of which his chance of winning a prize is $\frac{1}{100}$ . If the probability that he will win a prize exactly once is $\frac{1}{k}{\left(\frac{99}{100}\right)}^m$, then the value of $k+m$ is 

A person buys a lottery ticket in $50$ lotteries, in each of which his chance of winning a prize is $\frac{1}{100}$. If the probability that he will win a prize at least once is  $\mathrm{x}-{\left(0.\mathrm{y}\right)}^{50}$, then find the value of $\mathrm{x}+\mathrm{y}$.

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Suppose $\mathrm{X}$ has a binomial distribution $\mathrm{B}\left(6,\frac{1}{2}\right)$. Show that $\mathrm{X}=3$ is the most likely outcome.

In an examination, $20$ questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true'; if it falls tail, he answers 'false'. Find the probability that he answers at least $12$ questions correctly.

A bag consists of $10$ balls each marked with one of the digits $0 \mathrm{to} 9$. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit $0$?

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs at least one will fuse after $150$ days of use. [Write the answer up to four decimal places].

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs more than one will fuse after $150$ days of use. (round up to three decimal places)

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs not more than one will fuse after $150$ days of use. [Write the answer correct up to $3$ decimal places].

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. If the probability of out of $5$ such bulbs none will fuse after $150$ days of use is ${\left(0.95\right)}^k$. Then, find the value of $k$.

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the value of $k$, if probability that none is a spade will be $\frac{k}{1024}$?

Five cards are drawn successively with replacement from a well-shuffled deck of $52$cards. What is the value of $k$, if probability that only $3$ cards are spades is $\frac{k}{512}$?

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the value of $k$, if the probability that all the five cards are spades is $\frac{1}{k}$?